Economic historians have long looked to the English Revolution of 1688–1689 for an explanation of the political stability that encouraged industrial development. Now we are asked by William Deringer to see an additional benefit: public political contestation (and not the state's “instrumental desire for numerical information”) aroused an energy put increasingly into disputes about calculation (p. 13). The landowning seemed particularly suspicious of fancy calculations, regarding them as unmanly or trivial. Even Robert Boyle, son of a very landed earl, found mathematics esoteric and abstract, we are told. This account leaves out the fact that his opponent, Thomas Hobbes, wanted the new scientific culture to be mathematical and not experimental, hence less dangerous to royal order and power. Boyle had no animus against mathematics as such, but he was deeply suspicious of monarchical absolutism.
Bringing the history of science and mathematics into service as explanatory of “the rise of calculation in British civic epistemology” is indeed useful—if it is well done (p. 22). There are pitfalls, however. The fashion in science studies at the moment is never to credit change or improvement in science to the possibility that a discovery might just have been truer than its alternative. Rather than positioning the relative truth of numbers offering an avenue for commercial and industrial improvement, and hence their increasing importance and popularity, this book argues that the Revolution of 1688–1689 opened the partisan floodgates and made “numerical calculation” the object of “fear, animosity and distrust” (p. 28). The implication is that the more mathematically ignorant set the tone for political dispute; no set of figures escaped disputation. Just about any issue could turn polemical: the state of national revenues and expenditures, the payment of an equivalency to compensate the Scots for raising their taxes as a result of the 1707 union, the balance of trade with France, and not least, the national debt. The devastation wrought by the collapse in 1720 of the South Sea Bubble only raised the importance of calculation, and more controversy ensued.
Eventually not just the big cities but any hamlet could be used to produce “new data on the people, prosperity and produce of the countryside” (p. 268). Neither Ireland nor the American colonies were spared while both pessimists and optimists weighed in on the issue of an imagined depopulation. Luminaries like Richard Price, Arthur Young, and Benjamin Franklin joined the debate and gradually actuarial tables resulted. Moralists brought numbers and calculations to issues like social happiness, poverty, and alcoholism. Using numbers to advance political or moral agendas fostered “the emerging belief that numbers and calculations were a distinctly stubborn, honest, and incisive way of making public knowledge” (p. 301). The reader might well wonder why the landed and the Country opposition did not win the day and permanently consign mathematics to the categories of effete or esoteric.
There is considerable originality in this book on calculations and their discontents. The topic is fresh and the sources used are not obvious ones. Like many ambitious endeavors by talented historians, the book at moments sounds monocausal. If political contestation is the only key that explains the rising interest in calculation, how can we explain the early and increasing recourse to expertise? In just the first decade of the century, experts in science and commerce—the Newtonian David Gregory and the Scottish financier William Paterson—took up the challenge posed by calculating and explaining the great project of the Equivalent due to the Scots. The career of Gregory, who is depicted here simply as an “outsider,” is reduced to his politics when in fact the accusations against him in Edinburgh centered on his assumed irreligion and his use of the new science to support it. Had the possibility of the mathematically truthful not been a shared value, why turn to a practitioner so controversial, even if widely regarded as the finest mathematician in Scotland?
English commerce and science put the necessity to understand calculations front and center in the secondary school curricula. Multiple French spies and observers reported home on the “perfection of the English” in mathematical education (Roederer MSS, 29 AP 75, 395, Archives Nationales, Paris). The result became a race to try to catch up with an assumed British superiority in mechanics and its application. To compete, French school and college curricula were revised, and by 1800, scientific education laid emphasis on mechanics and calculations and then on their industrial application.
By that date the French had a lot of catching up to do. In the later decades of the century, committees of the House of Lords, charged with approving canal bills, took expert testimony from engineers as they tried to assess the effects of water diversion on local water-powered manufacturing. English lords interrogated the theories and practices by which the experts arrived at their calculations. Opponents of the proposed canal contested the figures and sometimes even hired their own engineers. By 1800 in Britain everything from canal building to steam-driven factories and mines required experts. The wrong-sized steam engine could bankrupt a business.
Many factors contributed to the rise of, and fury over, calculations. To be sure, political contestation played a significant role, but so too did the needs of commerce and manufacturing. Not least, we must factor in the extraordinary impact of Newtonian mechanics and its many applications. In that sense, 1687 and the publication of Newton's Principia should be added to 1688–1689 as benchmarks in the rise of mathematics as well as political contention. Knowledge of calculation added another weapon to the “rage of party” arsenal. More important, it also helped to make Britain into the first industrial knowledge economy.
